Question

Evidence suggests that 60% of USF students like turtles. Suppose we randomly sampled 9 USF students. Assume the binomial requirements are met. What is the probability 5 or fewer like turtles?

Answer 1

`P(X\leq 5)=0.5173`

Explanation:

-This is a binomial probability distribution problem.

-The probability of 5 or fewer can be calculated as:

`P(X=x)={n\choose x}p^x(1-p)^(n-x)\\\\P(X\leq 5)=P(X=0)+P(X=1)+...+P(X=5)\\\\\\={9\choose 0}0.6^0(1-0.6)^(9)+{9\choose 1}0.6^1(0.4)^(8)+{9\choose 2}0.6^2(0.4)^(7)++{9\choose 3}0.6^3(0.4)^(6)+{9\choose 4}0.6^4(0.4)^(5)+{9\choose 5}0.6^5(0.4)^(4)\\\\=0.0003+0.0035+0.0212+0.0743+0.1672+0.2508\\\\\\=0.5173`

Hence, the probability of 5 or fewer like turtles is 0.5173